Talk:Integral of inverse functions

Questionable content
This article was created on December 17, 2013. Its initial source was a paper published on Arxiv (which is not a journal, but a preprint repository) four days earlier, on December 13, 2013, by a researcher with apparently no academic affiliation. The paper contains a proof of the formula (using the Stieltjes integral) that it seems to present as if it were new, when in fact this is a simple exercise in an undergraduate analysis textbook of the 1960s (Burkill, *A Second Course in Mathematical Analysis*, Section 6.7, Exercise 6), and was no doubt known before then.

I am no longer an active editor on Wikipedia, but I wanted to draw editors' attention to the fact that one of the primary references in this article is of dubious reliability and, judging by appearances, may well have been introduced by an editor with a vested interest.24.50.177.199 (talk) 02:26, 15 June 2017 (UTC)

I will add that a French Wikipedian with the same username ("Maimonid") as the one who created the English article became engaged some time ago in debates about the corresponding French one. In particular, on April 9, 2014, he wrote:

Je ne parlerai pas de mon expérience personnelle, ni du fait que des mathématiciens que j'ai interrogés il y a environ 10 ans l'ignoraient et en furent surpris, bien que plus âgés et bien supérieurs a moi. "I won't mention my own experience or the fact that mathematicians I questioned some ten years ago were unaware of it and surprised by it, even though they were far older and better than I was." 

Compare this with the text of the paper on Arxiv: ''The author of the present article, which was unaware of the papers of Laisant and Key, was lead to the same result by simple geometric considerations in 1999. He then asked several mathematicians (some of renown) if this theorem was not unknown to them. They replied that they are unaware of any previous statement of this theorem, and that they are rather surprised that such elementary a result is not included in any introducing book of calculus.''

This evidence suggests strongly that the author of the non-peer-reviewed Arxiv paper is the same person who created the Wikipedia article and cited the paper. 24.50.177.199 (talk) 05:56, 15 June 2017 (UTC)

I concur that this is of questionable content, but for different reasons. If you spend some thought about the content of the theorem, you will realise that this is nothing other than the age old "Integration by Parts" theorem, known to the pioneers. So, the mathematicians involved have failed to realise the most basic connections within their own field, which is worrisome. However, I would prefer that the link between Integration by Parts theorem and inverse functions, and also product rule of differentiation, to be explicitly made clear, so that these confusions will stop happening. Also, this new viewpoint has already been fruitful, as it suggests to mathematicians to try working out the conditions for its validity. i.e. I question the claim of novelty, but grant them that it is original and useful and true. 111.65.71.144 (talk) 21:43, 23 November 2019 (UTC)